Honours Research Meeting
September 4, 2025
No results to summarise at this point; instead, I’m going to talk about:
Using the Longitudinal Business Database (LBD), which provides administrative firm-level data…
\[\text{Gross Output} = f(\text{Capital}, \text{Labour}, \text{Intermediates}) \times \text{TFP}\]
Data-prep
Competition directly affect on productivity, induceing firms to adopt some characteristics commensurate with productivity (e.g., R&D, managerial talent)
Competition leads to selective attrition of low-productivity firms: More-efficient firms accumulate market share, forcing the exit of less-efficient firms
To disentangle the two effects, I’m adapting 2 methods from Backus1:
| Source of endogeneity | Mitigation |
|---|---|
| Reverse causality (simultaneity) | IV: demand shifters (strong first stage) |
| Omitted variables | Firm FE + market trends; IV (demand/policy shocks) |
| Measurement confounds (TFPR) | Careful deflators; note TFPR ≠ pure technology |
Olley-Pakes decomposition splits market-level productivity into unweighted mean & covariance term that captures reallocation across survivors:
OP shows us upon which margin competition affects productivity, but within the mean it cannot separate treatment from selection
| Market Size | Sample Draw | “10th percentile” | “90th percentile” |
|---|---|---|---|
| \(n\) = 3 | [-0.5, 0.2, 1.1] | -0.5 (min) | 1.1 (max) |
| \(n\) = 6 | [-1.2, -0.3, 0.1, 0.4, 0.8, 1.5] | -1.2 (min) | 1.5 (2nd largest) |
Key insight: “Same” quantiles are different order statistics!
Bias: Larger \(n\) \(\rightarrow\) more extreme minimums \(\rightarrow\) “10th percentile” looks mechanically worse
Solution: Add polynomial in \(n\) to purge mechanical dependence
Thanks to Yiğit Sağlam for his supervision, Tim Ng for his support, and to Richard Fabling and Dave Maré pioneering work and balanced panels.
All mistakes, regrettably, are my own.
\[\ln y_{itj} = \beta^{(j)}_K \ln K_{itj} + \beta^{(j)}_L \ln L_{itj} + \beta^{(j)}_M \ln M_{itj} + \tau^{(j)}_t + \mu^{(j)}_i + \varepsilon_{itj}.\]
Two-stage model:
\[ \begin{align} X &= \pi Z + \Gamma W + v \quad \text{(first stage)} \\ Y &= \beta X + \delta' W + u \quad \text{(second stage)} \end{align} \]
Relevance: \(\pi \neq 0\).
Exclusion: \(Z \perp u\) and no path \(Z \to Y\) except through \(X\).
| Type | Measure | Description |
|---|---|---|
| Structure | HHI | Weighted measure of market concentration Larger ⇒ weaker competition |
| Power | PCM | Percentage markup over costs Higher ⇒ weaker competition |
| Power | PE | How strongly cost increases reduce profits (negative values) Smaller negative ⇒ weaker competition (profits less sensitive to costs) Larger negative ⇒ stronger competition (profits more sensitive) |
\[\text{HHI}_{X,jt} = \frac{\sum_{i=1}^{N_jt} X_{ijt}^2}{(\sum_{i=1}^{N_jt} X_{ijt})^2}, X \in \{Y, L\}\]
Average PCM \[\text{PCM}_{jt} = \frac{1}{N_{jt}}\sum_{i=1}^{N_{jt}}\max\left\{\frac{Y_{ijt} - C_{ijt}}{Y_{ijt}}, -1\right\}\]
Aggregate PCM \[\text{PCM}_{A,jt} = \frac{\sum_{i=1}^{N_{jt}}(Y_{ijt} - C_{ijt})}{\sum_{i=1}^{N_{jt}} Y_{ijt}}\]
\[\ln(Y_{ijt} - C_{ijt}) = \alpha_{j't} + \text{PE}_{jt} \times \frac{C_{ijt}}{Y_{ijt}} + \epsilon_{ijt}\]